Question

The product of two rational numbers is (a rational, an irrational) number because multiplying two rational numbers is equivalent to the ratio of (2 integers, a rational number and an irrational number, two irrational numbers), which is (a rational, an irrational).

A) A rational; 2 integers; a rational
B) A rational; a rational number and an irrational number; an irrational
C) An irrational; 2 integers; an irrational
D) An irrational; a rational number and an irrational number; a rational

Answer 1

The product of two rational numbers is a rational number because it is the ratio of two integers. Option A correctly represents this: A rational; 2 integers; a rational.

Step-by-step explanation:

The product of two rational numbers is a rational number because multiplying two rational numbers is equivalent to the ratio of two integers, which is a rational. Rational numbers include fractions, which are expressed as the ratio of two integers (where the denominator is not zero). When we multiply two such fractions, we multiply their numerators and denominators respectively, resulting in another fraction that is also the ratio of two integers.

For example, multiplying ½ by ¾ gives ½ × ¾ = (1×3)/(2×4) = 3/8, which is another rational number. Hence, the correct answer to the student's question is A) A rational; 2 integers; a rational.